There is known a two-wheeled vehicle including a rear arm having a generally triangular side elevation, and having a rear end on which a rear wheel is rotatably mounted, a main frame on which the front end of the rear arm is rotatably supported, and a suspension mechanism mounted between the top of the rear arm and the main frame. If a large suspension mechanism is employed in a vehicle having such a suspension mechanism, it is necessary to provide a space for mounting it therein at the sacrifice of space for the main frame. This should, however, not be permitted to result in reduced rigidity of the main frame. Therefore, provision must be made for preventing reduction in the rigidity of the main frame.